Missing values estimation and consensus building for incomplete hesitant fuzzy preference relations with multiplicative consistency

This paper proposes a decision support process for incomplete hesitant fuzzy preference relations (HFPRs). First, we present a revised definition of HFPRs, in which the values are not ordered for the hesitant fuzzy element. Second, we propose a method to normalize the HFPRs and estimate the missing elements in incomplete HFPRs based on multiplicative consistency. Based on this, a consensus model with incomplete HFPR is developed. A feedback mechanism is proposed to obtain a best choice with desired consensus level. Multiplicative consistency induced ordered weighted averaging (MC-IOWA) operator is used to aggregate the individual HFPRs into a collective one. A score HFPR is proposed for collective HFPR, and then the hesitant quantifier-guided non-dominance degrees (HQGNDD) of alternatives by using an OWA operator are obtained to rank the alternatives. Finally, a case study for evaluate the qualification of supply chain enterprises is provided to illustrate its application.